Imaging the conductance of integer and fractional quantum hall edge states

Physical Review X

Volumn 4, Issue 1, 2014, Pages

  Pascher, Nikola ^a   Rössler, Clemens ^a   Ihn, Thomas ^a   Ensslin, Klaus ^a   Reichl, Christian ^a   Wegscheider, Werner ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Nanophysics; Strongly correlated materials

Indexed keywords

ELECTRON GAS; INCOMPRESSIBLE FLOW; QUANTUM CHEMISTRY;

FRACTIONAL FILLING; HALL RESISTANCE; INHOMOGENEITIES; MEAN FREE PATH; MICROSCOPIC INHOMOGENEITIES; NANOPHYSICS; QUANTUM POINT CONTACT; STRONGLY CORRELATED MATERIALS;

QUANTUM THEORY;

EID: 84900328510     PISSN: None     EISSN: 21603308     Source Type: Journal    
DOI: 10.1103/PhysRevX.4.011014     Document Type: Article

References (51)

1. K. V. Klitzing, G. Dorda, and M. Pepper, New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance, Phys. Rev. Lett. 45, 494 (1980).
2. D. C. Tsui, H. L. Stormer, and A. C. Gossard, Two-Dimensional Magnetotransport in the Extreme Quantum Limit, Phys. Rev. Lett. 48, 1559 (1982).
3. B. I. Halperin, Quantized Hall Conductance, Current-Carrying Edge States, and the Existence of Extended States in a Two-Dimensional Disordered Potential, Phys. Rev. B 25, 2185 (1982).
4. M. Büttiker, Absence of Backscattering in the Quantum Hall Effect in Multiprobe Conductors, Phys. Rev. B 38, 9375 (1988).
5. D. B. Chklovskii, B. I. Shklovskii, and L. I. Glazman, Electrostatics of Edge Channels, Phys. Rev. B 46, 4026 (1992).
6. C.W. J. Beenakker and H. van Houten, in Semiconductor Heterostructures and Nanostructures, Solid State Physics, Vol. 44, Henry Ehrenreich and David Turnbull (Academic Press, New York, 1991) pp. 1-228.
7. J. Dempsey, B. Y. Gelfand, and B. I. Halperin, Electron-Electron Interactions and Spontaneous Spin Polarization in Quantum Hall Edge States, Phys. Rev. Lett. 70, 3639 (1993).
8. S. Ihnatsenka and I. V. Zozoulenko, Spatial Spin Polarization and Suppression of Compressible Edge Channels in the Integer Quantum Hall Regime, Phys. Rev. B 73, 155314 (2006).
9. J. Weiss and K. von Klitzing, Metrology and Microscopic Picture of the Integer Quantum Hall Effect, Phil. Trans. R. Soc. A 369, 3954 (2011).
10. A. M. Chang, A Unified Transport Theory for the Integral and Fractional Quantum Hall Effects: Phase Boundaries, Edge Currents, and Transmission/Reflection Probabilities, Solid State Commun. 74, 871 (1990).
11. A. H. MacDonald, Edge States in the Fractional-Quantum-Hall-Effect Regime, Phys. Rev. Lett. 64, 220 (1990).
12. X. G. Wen, Electrodynamical Properties of Gapless Edge Excitations in the Fractional Quantum Hall States, Phys. Rev. Lett. 64, 2206 (1990).
13. B. Y. Gelfand and B. I. Halperin, Edge Electrostatics of a Mesa-Etched Sample and Edge-State-to-Bulk Scattering Rate in the Fractional Quantum Hall Regime, Phys. Rev. B 49, 1862 (1994).
14. C. de C. Chamon and X. G. Wen, Sharp and Smooth Boundaries of Quantum Hall Liquids, Phys. Rev. B 49, 8227 (1994).
15. X. Wan, K. Yang, and E. H. Rezayi, Reconstruction of Fractional Quantum Hall Edges, Phys. Rev. Lett. 88, 056802 (2002).
16. K. Yang, Field Theoretical Description of Quantum Hall Edge Reconstruction, Phys. Rev. Lett. 91, 036802 (2003).
17. R. J. F. van Haren, F. A. P. Blom, and J. H. Wolter, Direct Observation of Edge Channels in the Integer Quantum Hall Regime, Phys. Rev. Lett. 74, 1198 (1995).
18. R. Knott, W. Dietsche, K. Von Klitzing, K. Eberl, and K. Ploog, Electro-optic Imaging of Potential Distributions in the Quantum Hall Regime, Semicond. Sci. Technol. 10, 117 (1995).
19. Y. Y. Wei, J. Weis, K. V. Klitzing, and K. Eberl, Edge Strips in the Quantum Hall Regime Imaged by a Single-Electron Transistor, Phys. Rev. Lett. 81, 1674 (1998).
20. K. L. McCormick, M. T.Woodside, M. Huang, M.Wu, P. L. McEuen, C. Duruoz, and J. S. Harris, Scanned Potential Microscopy of Edge and Bulk Currents in the Quantum Hall Regime, Phys. Rev. B 59, 4654 (1999).
21. A. Yacoby, H. F. Hess, T. A. Fulton, L. N. Pfeiffer, and K.W. West, Electrical Imaging of the Quantum Hall State, Solid State Commun. 111, 1 (1999).
22. G. Finkelstein, P. I. Glicofridis, R. C. Ashoori, and M. Shayegan, Topographic Mapping of the Quantum Hall Liquid Using a Few-Electron Bubble, Science 289, 90 (2000).
23. R. J. Haug, Edge-State Transport and Its Experimental Consequences in High Magnetic Fields, Semicond. Sci. Technol. 8, 131 (1993).
24. A. M. Chang and J. E. Cunningham, Transmission and Reflection Probabilities between ν = 1 and ν = 2/3 Quantum Hall Effects and between ν = 2/3 and ν = 1/3 Effects, Solid State Commun. 72, 651 (1989).
25. L. P. Kouwenhoven, B. J. van Wees, N. C. van der Vaart, C. J. P.M. Harmans, C. E. Timmering, and C .T. Foxon Selective Population and Detection of Edge Channels in the Fractional Quantum Hall Regime, Phys. Rev. Lett. 64, 685 (1990).
26. B. J. van Wees, E. M. M. Willems, C. J. P. M. Harmans, C.W. J. Beenakker, H. van Houten, J. G. Williamson, C. T. Foxon, and J. J. Harris, Anomalous Integer Quantum Hall Effect in the Ballistic Regime with Quantum Point Contacts, Phys. Rev. Lett. 62, 1181 (1989).
27. B. R. Snell, P. H. Beton, P. C. Main, A. Neves, J. R. Owers-Bradley, L. Eaves, M. Henini, O. H. Hughes, S. P. Beaumont, and C. D.W. Wilkinson, Quantised Hall effect and Magnetoresistance Through a Quantum Point Contact, J. Phys. Condens. Matter 1, 7499 (1989).
28. F. P. Milliken, C. P. Umbach, and R. A.Webb, Indications of a Luttinger Liquid in the Fractional Quantum Hall Regime, Solid State Commun. 97, 309 (1996).
29. D. C. Glattli, H. Rodriguez, V. Perrin, P. Roche, Y. Jin, and B. Etienne, Shot Noise and the Luttinger Liquid-like Properties of the FQHE, Physica (Amsterdam) E 6, 22 (2000).
30. S. Roddaro, V. Pellegrini, F. Beltram, G. Biasiol, L. Sorba, R. Raimondi, and G. Vignale, Nonlinear Quasiparticle Tunneling between Fractional Quantum Hall Edge, Phys. Rev. Lett. 90, 046805 (2003).
31. N. Aoki, C. R. da Cunha, R. Akis, D. K. Ferry, and Y. Ochiai, Imaging of Integer Quantum Hall Edge State in a Quantum Point Contact via Scanning Gate Microscopy, Phys. Rev. B 72, 155327 (2005).
32. N. Paradiso, S. Heun, S. Roddaro, L. Sorba, F. Beltram, G. Biasiol, L. N. Pfeiffer, and K.W. West, Imaging Fractional Incompressible Stripes in Integer Quantum Hall Systems, Phys. Rev. Lett. 108, 246801 (2012).
33. C. Rössler, S. Baer, E. de Wiljes, P. L. Ardelt, T. Ihn, K. Ensslin, C. Reichl, and W. Wegscheider, Transport Properties of Clean Quantum Point Contacts, New J. Phys. 13, 113006 (2011).
34. A. E. Gildemeister, T. Ihn, M. Sigrist, K. Ensslin, D. C. Driscoll, and A. C. Gossard, Measurement of the Tip-Induced Potential in Scanning Gate Experiments, Phys. Rev. B 75, 195338 (2007).
35. N. Paradiso, S. Heun, S. Roddaro, L. N. Pfeiffer, K.W. West, L. Sorba, G. Biasiol, and F. Beltram, Selective Control of Edge-Channel Trajectories by Scanning Gate Microscopy, Physica (Amsterdam) E 42, 1038 (2010).
36. M. E. Suddards, A. Baumgartner, M. Henini, and C. J. Mellor, Scanning Capacitance Imaging of Compressible and Incompressible Quantum Hall Effect Edge Strips, New J. Phys. 14, 083015 (2012).
37. V. Venkatachalam, A. Vacoby, L. Pfeiffer, and K. West, Local Charge of the ν = 5/2 Fractional Quantum Hall State, Nature (London) 469, 185 (2011).
38. A conceptually similar situation arises in the context of C-V profiling [50], where a differential measurement of the capacitance versus voltage leads to the extraction of an electron density profile. Even when applied to a quantized system, the results that are based on a classical theory roughly reflect the true quantum-mechanical density distribution (an example is shown in [51]). In analogy, we may roughly (but not strictly) see our dI/dx derivative as a current density profile.
39. D. B. Chklovskii, Structure of Fractional Edge States: A Composite-Fermion Approach, Phys. Rev. B, 51, 9895 (1995).
40. C.W. J. Beenakker, Edge Channels for the Fractional Quantum Hall Effect, Phys. Rev. Lett. 64, 216 (1990).
41. N. Paradiso, S. Heun, S. Roddaro, G. Biasiol, L. Sorba, D. Venturelli, F. Taddei, V. Giovannetti, and F. Beltram, Imaging Backscattering through Impurity-Induced Antidots in Quantum Hall Constrictions, Phys. Rev. B 86, 085326 (2012).
42. F. Martins, S. Faniel, B. Rosenow, H. Sellier, S. Huant, M. G. Pala, L. Desplanque, X. Wallart, V. Bayot, and B. Hackens, Coherent Tunnelling across a Quantum Point Contact in the Quantum Hall Regime, Sci. Rep. 3, 1416 (2013).
43. G. A. Steele, R. C. Ashoori, L. N. Pfeiffer, and K.W. West, Imaging Transport Resonances in the Quantum Hall Effect, Phys. Rev. Lett. 95, 136804 (2005).
44. L. Cockins, Y. Miyahara, S. D Bennett, A. A. Clerk, S. Studenikin, P. Poole, A. Sachrajda, and P. Grutter, Energy Levels of Few-Electron Quantum Dots Imaged and Characterized by Atomic Force Microscopy, Proc. Natl. Acad. Sci. U.S.A. 107, 9496 (2010).
45. R. Willett, J. P. Eisenstein, H. L. Störmer, D. C. Tsui, A. C. Gossard, and J. H. English, Observation of an Even-Denominator Quantum Number in the Fractional Quantum Hall Effect, Phys. Rev. Lett. 59, 1776 (1987).
46. K.-F. Berggren, G. Roos, and H. van Houten, Characterization of Very Narrow Quasi-One-Dimensional Quantum Channels, Phys. Rev. B 37, 10118 (1988).
47. D. B. Chklovskii, K. A. Matveev, and B. I. Shklovskii, Ballistic Conductance of Interacting Electrons in the Quantum Hall Regime, Phys. Rev. B 47, 12605 (1993).
48. H. A. Fertig and B. I. Halperin, Transmission Coefficient of an Electron through a Saddle-Point Potential in a Magnetic Field, Phys. Rev. B 36, 7969 (1987).
49. M. Büttiker, Quantized Transmission of a Saddle-Point Constriction, Phys. Rev. B 41, 7906 (1990).
50. J. Hilibrand and R. D. Gold, Determination of Impurity Distribution in Junction Diodes from Capacitance-Voltage Measurements, RCA Rev. 21, 245 (1960).
51. T. Ihn, K. J. Friedland, R. Hey, and F. Koch, Magnetotransport Phenomena in Periodically δ-Doped Structures, Phys. Rev. B 52, 2789 (1995).